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Question
If X has a binomial distribution with n = 20 , p = `1/10` , find E (X) and V (X).
Solution
Given X ~ B(n, p)
Where n = 20 , p = `1/10`
P + q = 1
∴ q = 1 - p = `1-1/10 = 9/10`
∴ n = 20 , p = `1/10` , q = `9/10`
Mean= E(x) = np =`20 xx 1/10 = 2`
Variance = V(x) = npq = `20 xx 1/10 xx 9/10`
`= 18/10 = 1.8`
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